Unilateral vs Bilateral CVA

[Pom]

Hi David,

I have read about unilateral and bilateral CVA from the GARP study material Ch 15 Pg 350-351 example & table 15-5.
The whole explanation and logic was clear to me.

However, on reading the BT notes pg 176 & 177 I am bit lost.
CVA(Bilateral) = Ea.Sa -Eb.Sb
2 interpretations I had to make due to lack of clarity/lack of 100% understanding:
a) In the example, there is no upfront mention of when the trade was done which CPTY is in the money and who is out of the money.. (I had to conclude by looking at the final green box where it is mentioned that Bank A will value the portfolio at -$3xx, mid market for Bank A will be -$300)
b) Ea is defined as Discounted Expected Exposure faced by B with respect to A.
This means that when Bank A is doing it's calculations on how much NEE they have against Bank B they come up with $1000 number and the Loss Rate of 1% (Sa) is the % amount of money lost after recovery when Bank A going bust. Thus the formula BT formula seems to have the signs switched to equation 15.5 in Pg 349 of GARP study material.

Before jumping to the above equation, I would like to think how would the Unilateral CVA charge would have been done.
In case of unilateral CVA charge from Bank A perspective would be $500 x 4% = $20. This the expected amount bank A looses if CPTY B defaults.
Thus as understood from GARP Study Material, I would intuitively think from Bank A perspective that Bank A would charge CPTY B $20 as CVA. Hence if the portfolio value is -$300 (Bank A owe $300 to CPTY B, in the books it will reflect that Bank A owes only $280 as it will charge the CPTY for it's poor credit risk).

Now coming to the Bilateral CVA intuitively I have understood that charging CPTY is not a one way street, we have to give benefit to the CPTY, for Bank A's credit worthiness as well.
Hence, $1000x1% stands for how much Bank A assumes CPTY B would loose if Bank A defaults.
Thus from Bank A perspective they can't charge $20 to CPTYB but only $10. Thus if the mid market for Bank A is -$300 then it should value the asset at -$290, still charging $10 to the client.
Thus, because of my above understanding I have been unable to solve the BT Qs intuitively.

Can you clarify the correctness of my 2 interpretations & how to work out the unilateral cva?
Further, as per the table on Pg177 in BT notes, if Bank A faces more credit risk than CPTY B, then effect is value of OTC derivative reduces for Bank A. The word reduces here isn't clear to me, i.e. how should we treat the CVA to the portfolio value.

 

[David Harper CFA FRM]

Hi Pom, I have to bookmark this for later (sorry, it deserves careful time, i think!).

Quick question, where is Ch 15 Table 15-5; i.e., is that a Jon Gregory Chapter?
(GARP doesn't create any of its own material to my knowledge, this is an assigned reading i assume?)

Would you mind referencing the source material b/c I own all of the sources, and I am not sure what "Chapter 15" refers to, I assume it is among:

39. Jon Gregory, Counterparty Credit Risk: The New Challenge for Global Financial Markets
• Chapter 2.............................Defining Counterparty Credit Risk
• Chapter 3.............................Mitigating Counterparty Credit Risk
• Chapter 4.............................Quantifying Counterparty Credit Exposure, I
• Chapter 5.............................Quantifying Counterparty Credit Exposure, II: The Impact of Collateral

Suzanne Evans if you get a chance to look at this, notice Pom has referenced Ch 15 Pg 350-351 of the GARP Study Materials, but that must correspond to some T6. Credit Risk reading, but I am not familiar with such a numbering system, I guess GARP has re-numbered the readings in their re-packaging? ... but what's weird to me is the Table 15-5 implies there is a Chapter 15 somewhere, but i don't see any Chapter 15 is T6

 

[Pom]

Hi David,
My appologies, GARP material has labelled all the readings as Chapter nos..

http://www.garp.org/media/1106184/frm_study_guide_changes_2013.pdf

I am refering to reading :Jon Gregory, Counterparty Credit Risk: The New Challenge for Global Financial Markets. chapter 7 Pricing Counterparty Credit Risk I.
The table I am refering to in this reading is - Unilateral & Bilateral CVA values for Case A & Case B under assumption of independence of default and no wrong way risk.

On further thought, I realise that the notes are covering something which is not in the syllabus any more. Thus I haven't read the reading to which this formula belongs to. I still need to understand on how you would solve the example after reading Chapter 7.

Regards
Anupam

 

[David Harper CFA FRM]

Hi Anupam - oh, okay, i'll look when i can but I can't imagine in will change the solution, the new Gregory CVA is a more detailed version of the same CVA that is explained in much simpler terms in the previous Canabarro. Gregory takes it further, but a fundamental conflict (i.e., a conflict in the basic definition of CVA/BCVA) is highly unlikely, i bookmarked b/c i have very little spare time currently but will get to this asap, thanks,

 

[desert_rain]

Hi David,

I am in the same boat as the original poster and was wondering if you have had a chance to look into this. Based on Gregory's chapter, a positive BCVA from Party A's perspective implies that party A faces more Counterparty risk than its counterparty and whereas if I understood the example (the table at the top of the page) you provided in the BT notes pg 177 for Chapter 7 Pricing Counterparty Credit Risk, it is exactly the opposite. I understand the example is based on prior reading on Canabarro but I would really like to understand this conceptually. I did try to research this but that confounded my already confused state further.

Please help.

 

[David Harper CFA FRM]

Hi desert_rain,

Yes, I have had a chance (and actually it's in my upcoming feedback to GARP: I am sure they have zero idea). Canabarro and Gregory reverse the terms (consistent with your confusion). Here is the example I am have included for GARP (please note this may not be my final yet, I have asked another expert to review to check my conclusion):

• Gregory 7.3.4 (essentially a simplification of the BVCA but directionally consistent) highlights a basic example where the institution (call it 'A') has ENE of 3% and credit spread of 200 bps; the counterparty (call them 'B') has EPE of 5% and credit spread of 300 bps. The BVCA approximation is then given as (5%*300) - 3%*(200) = +11 bps
• If we applied the same circumstance to Canabarro (i.e., from the perspective of the institution 'A'), we would use CVA = E(A)*s(a) - E(B)*s(b) = 3%*(200) - (5%*300) - = -11 bps, because E(B) is the exposure faced by the institution (A), so basically the unilateral CVA, from the intitution's (A's) perspective is the first term (e.g., EPE not ENE) of Gregory but the second term of Canabarro

I don't want to be dramatic about it: it's not the first time a sign (+/-) doesn't spell a huge practical different. For example, in Canabarro the negative BCVA reduces the value of the trade; in Gregory, with economic similarity, it represents an amount the institution "may charge the counterparty ... effectively for the overall counterparty risk;" i.e., in both cases, the credit quality of the institution (A), faced by the counterparty (B), is better than the credit quality of the counterparty; put another way, institution (A) "faces more credit risk." I hope that explains, thanks,